Barry Richards - Academia.edu (original) (raw)

Philosophy of Language by Barry Richards

Research paper thumbnail of Rights and the Good Life Draft

Michael Sandel claims that “The attempt to detach arguments about justice and rights from argumen... more Michael Sandel claims that
“The attempt to detach arguments about justice and rights from arguments about the good life is mistaken for two reasons. First, it is not always possible to decide questions of justice and rights without resolving substantive moral questions; and second, even where it’s possible, it may not be desirable.”
We consider three examples which Sandel cites to illustrate where rights cannot be resolved without resolving moral or theological questions. If the disputes involved in these examples are intrinsically unresolvable, Sandel’s claim suggests that the rights at issue are also intrinsically unresolvable. Considerations of the good life do not have a role here.

Research paper thumbnail of Adverbs - From a logical point view.pdf

To give the logical form of a sentence is to specify among other things the relative scope of eac... more To give the logical form of a sentence is to specify among other things the relative scope of each of its logically significant non-sentential expressions. We suggest that there are two basic types of adverbs, those that modify formulas and those that modify verbs. To revel their distinct logical properties we extend first-order logic by adding operators of the appropriate sort. However, we do not treat the resulting system as an intensional logic, nor dowe resort to an intensional ontology or an ontology of events.

Research paper thumbnail of On interpreting pronouns

Linguistics and Philosophy, 1984

Research paper thumbnail of Anaphora, descriptions and discourse representations

Research paper thumbnail of A point of reference

Synthese, 1974

If we could recover our pre-Fregean semantic innocence, I think it would seem to us plainly incre... more If we could recover our pre-Fregean semantic innocence, I think it would seem to us plainly incredible that the words 'The earth moves', uttered after the words 'Galileo said that', mean anything different, or refer to anything else, than is their wont when they come in other environments.* Frege would have us believe that in any utterance of the sentence 'The earth moves and Galileo said that the earth moves', the referents of the two occurrences of 'the earth' are necessarily distinct. Davidson reminds us, however, that such referential ambiguity is genuinely counterintuitive. A similar objection applies to Quine's theory of referential opacity. Quine would have us treat singular terms in modal (or oblique) contexts as if they were under quotation. In effect, he would have us take 'the earth' when it occurs in 'Galileo said that the earth moves' to be essentially like its occurrence in' "The earth" has eight characters'. Expressions under quotation are, according to Quine, referentially inert, i.e. they neither refer nor can be used to refer. Hence, in any utterance of 'The earth moves and Galileo said that the earth moves' only the first occurrence of 'the earth' is genuinely referential. But clearly, this theory is no less incredible than is Frege's; Davidson's objection is equally applicable here.

Artificial Intelligence by Barry Richards

Research paper thumbnail of AI AGENTS

Research paper thumbnail of Towards a closer integration of finite domainpropagation and simplex-based algorithms

This paper describes our experience in implementing an industrial application using the finite do... more This paper describes our experience in implementing an industrial application using the finite domain solver of the ECL i PS e constraint logic programming (CLP) system, in conjunction with the mathematical programming (MP) system, FortMP. In this technique, the ECL i PS e system generates a feasible solution that is adapted to construct a starting point (basic solution) for the MP solver. The basic solution is then used as an input to the FortMP system to warm-start the simplex (SX) algorithm, hastening the solution of the linear programming relaxation, (LPR). SX proceeds as normal to find the optimal integer solution.

Research paper thumbnail of Nonsystematic Search and No-Good Learning

Journal of Automated Reasoning, 2000

Nonsystematic search algorithms seem, in general, to be well suited to large-scale problems with ... more Nonsystematic search algorithms seem, in general, to be well suited to large-scale problems with many solutions. However, they tend to perform badly for problems with few solutions, and they cannot be used for insoluble problems, since they are incomplete.

Drafts by Barry Richards

Research paper thumbnail of Another Point of Reference

Expressions are usually distinct from their semantics; that is, expressions themselves do not par... more Expressions are usually distinct from their semantics; that is, expressions themselves do not participate in their semantics. One exception is where expressions are quoted. The conjecture below is that there are other contexts in which expressions participate in their semantics, even though they are not quoted or mentioned in any way. Propositional attitudes are one example, and the way they contain singular propositions generates a number of questions, among them the following. • Do demonstratives and names contribute to ascribed beliefs in the same way? • What contribution does an indexical make to the content of a belief or a thought? • Does Semantic Relationism capture the content of a name when it occurs in ascribed beliefs? • If names have sense, can that sense be understood as a procedure rendered as a program? • Does machine learning show how the referent of a name can be learnt without invoking either sense or direct reference? A number of conjectures emerge from considering these questions, and it is shown that they can be implemented jointly in a consistent logical system.

Research paper thumbnail of Language of Thought and Cognitive Science

Fodor and Pylyshyn propose an approach to the study of mind where semantic concepts, with the exc... more Fodor and Pylyshyn propose an approach to the study of mind where semantic concepts, with the exception of reference, can have no fundamental explanatory role. 1 Their claim reflects a view of cognitive science where mental processes are computations over tokens of mental representations, i.e., over their physical renderings. These cause behaviour and provide an explanation of it. The problem, to be shown below, is that mental representations can have an ambiguous status depending on the context. Resolving the ambiguity is an intractable task. This threatens Fodor and Pylyshyn's approach to cognitive science.

Papers by Barry Richards

Research paper thumbnail of Constraint logic programming for scheduling and planning

BT technology journal, 1995

Constraint Logic Programming languages are extensions of logic programming systems such as PROLOG... more Constraint Logic Programming languages are extensions of logic programming systems such as PROLOG with constraint-handling facilities. There have been two lines of development: systems such as the CLP(X) scheme JL87] and PROLOG III Col90] in which constraints are ...

Research paper thumbnail of Planning parallel actions

Artificial Intelligence, 1998

This paper presents an integrated view of a wide range of planning systems derived from different... more This paper presents an integrated view of a wide range of planning systems derived from different theoretical foundations. The work is motivated by the need to provide a clear foundation from which a systematic study of search and representation issues in planning can be conducted. An evolutionary path is identified which shows how the classical (state-based) planning strategy can be incrementally refined into strategies capable of generating parallel plans. This is achieved by considering a succession of planning strategies having a progressively deeper involvement with interval-based representations. Each strategy is defined in terms of a plan representation, truth criterion and an example plan generation procedure which maps out a clearly specified search graph. The capabilities and limitations of each strategy are compared. This approach enables much of the wisdo'm embedded in existing planners based on the specified strategies to be distilled and unified. The succession of planning strategies identified in this paper define a framework within which fundamental design issues can be considered such as the level of commitment a constraintposting planner should make during its search for a solution. The framework also highlights the need for practical planners to prevent synergistic interference between parallel actions in an efficient manner. @ 1998 Elsevier Science B.V.

Research paper thumbnail of Distributed optimisation: A case study of utilising teaching space in a college

This paper presents an approach to distributed optimisation applied to the problem of teaching sp... more This paper presents an approach to distributed optimisation applied to the problem of teaching space utilisation in a college. We describe the basic ingredients of the problem and analyse various solutions, some produced in a centralised environment and some in a distributed environment. The main aim is to investigate how distributed optimisation may be formulated. In particular we introduce a "broker"-based approach for interdepartmental sharing of resources, with a view to finding a reasonable compromise between allowing a degree of autonomy for individual departments and optimising the global usage of resources at the college level. Various results of the experiments based on different optimisation criteria and heuristics are presented and analysed. 1 Introduction The problem of teaching space utilisation(TSU) addresses the task of making effective use of teaching space within a distributed college environment [2, 3, 4, 6, 7]. This involves scheduling timetables and allocating reso...

Research paper thumbnail of A Decomposition-based Approach to Checking the Satisfiability of Temporal Database Query in Temporal Planning

Journal of electrical engineering and information science, 1999

This paper presents a method for increasing the efficiency of checking the satisfiability of a st... more This paper presents a method for increasing the efficiency of checking the satisfiability of a structure known as a temporal database query(TDBQ), which is an essential component of temporal planning. We develop a new "qualitative" strategy for decomposing a TDBQ into nearly-independent sub-TDBQ's, whose satisfiability can be checked separately; if all sub-TDBQ's are satisfiable, we use an efficient method of testing for global consistency. To ensure the correctness of the procedure we must impose certain restrictions on the temporal constraints used in specifying planning problems and action operators. But these do not present an awkward restriction on expressiveness. They do, however, lead to a significant reduction in the propagation of constraints and thus greatly enhance the performance of the temporal reasoning system.

Research paper thumbnail of The Scope, order, and distribution of English auxiliary verbs

Table of Contents Volume two.- A New Theory of English Auxiliaries.- Scope Ambiguities of Tense, ... more Table of Contents Volume two.- A New Theory of English Auxiliaries.- Scope Ambiguities of Tense, Aspect and Negation.- Generalized Categorial Grammars and the English Auxiliary.- Auxiliary and Copula Be in a Functional Grammar of English.- Explaining Auxiliary Order.- Semantic Explanations for the Syntax of the English Modals.- The Auxiliary System in Sranan.

Research paper thumbnail of Linguistic Categories: Auxiliaries and Related Puzzles

Language, 1985

In the English grammar lessons, will and shall are taught in schools and universities as modal ve... more In the English grammar lessons, will and shall are taught in schools and universities as modal verbs. Almost all famous grammarians confirm that will and shall are modal verbs. Modal verbs are considered as auxiliaries apart from the main or primary auxiliaries be, have, and do. Considering the definitions and characteristics of auxiliaries and inflections, a deep understanding of will and shall is required. This paper examines the definitions and characteristics of both auxiliaries and inflections and the uses of will and shall in order to know whether will and shall are auxiliaries or free inflections of the Future Tense. However it is worth mentioning that time is divided into past, present, and future. In modern English, almost grammarians say that there are two tenses in English namely present tense and past tense. According to them, the future tense does not exist. They believe so simply because there is no inflection for future tense; the futurity is expressed through modal verbs (will and shall). Generally speaking, modal auxiliaries help lexical verbs to express a variety of meanings, different attitudes, such as mood, aspect, etc. whereas inflections help verbs to express tenses. For instance,-ed is a bound inflection that helps regular verbs express the simple past tense. The-s is also a bound inflection that expresses the third person singular in the Simple Present Tense whereas-Ø is an invisible inflection which expresses the first persons (singular and plural), second persons (singular and plural), and the third person plural of the Simple Present Tense). Is there any inflection for the Future Tense? This paper is an attempt to answer this question.

Research paper thumbnail of Semantic Theory and Grammatical Structure

Aristotelian Society Supplementary Volume, 1980

I. Introduction. What we discern as the grammatical structure of a language may depend in part up... more I. Introduction. What we discern as the grammatical structure of a language may depend in part upon considerations of semantic theory. This is particularly true if the grammar is categorial, for such a grammar can be seen to have a special connection with formal ...

Research paper thumbnail of Constructivism and logical reasoning

Synthese, 1985

Cognitive development is typically thought to be a process which involves the acquisition of new ... more Cognitive development is typically thought to be a process which involves the acquisition of new concepts. As a child progresses from infancy to maturity, he shows an increasing ability to deal with complex situations, and it is natural to account for this in terms of the addition of ...

Research paper thumbnail of Application of the Generic Planning Architecture to Flight Allocation

Research paper thumbnail of An Empirical Study of Min-Conflict Hill Climbing and Weak Commitment Search

Research paper thumbnail of Rights and the Good Life Draft

Michael Sandel claims that “The attempt to detach arguments about justice and rights from argumen... more Michael Sandel claims that
“The attempt to detach arguments about justice and rights from arguments about the good life is mistaken for two reasons. First, it is not always possible to decide questions of justice and rights without resolving substantive moral questions; and second, even where it’s possible, it may not be desirable.”
We consider three examples which Sandel cites to illustrate where rights cannot be resolved without resolving moral or theological questions. If the disputes involved in these examples are intrinsically unresolvable, Sandel’s claim suggests that the rights at issue are also intrinsically unresolvable. Considerations of the good life do not have a role here.

Research paper thumbnail of Adverbs - From a logical point view.pdf

To give the logical form of a sentence is to specify among other things the relative scope of eac... more To give the logical form of a sentence is to specify among other things the relative scope of each of its logically significant non-sentential expressions. We suggest that there are two basic types of adverbs, those that modify formulas and those that modify verbs. To revel their distinct logical properties we extend first-order logic by adding operators of the appropriate sort. However, we do not treat the resulting system as an intensional logic, nor dowe resort to an intensional ontology or an ontology of events.

Research paper thumbnail of On interpreting pronouns

Linguistics and Philosophy, 1984

Research paper thumbnail of Anaphora, descriptions and discourse representations

Research paper thumbnail of A point of reference

Synthese, 1974

If we could recover our pre-Fregean semantic innocence, I think it would seem to us plainly incre... more If we could recover our pre-Fregean semantic innocence, I think it would seem to us plainly incredible that the words 'The earth moves', uttered after the words 'Galileo said that', mean anything different, or refer to anything else, than is their wont when they come in other environments.* Frege would have us believe that in any utterance of the sentence 'The earth moves and Galileo said that the earth moves', the referents of the two occurrences of 'the earth' are necessarily distinct. Davidson reminds us, however, that such referential ambiguity is genuinely counterintuitive. A similar objection applies to Quine's theory of referential opacity. Quine would have us treat singular terms in modal (or oblique) contexts as if they were under quotation. In effect, he would have us take 'the earth' when it occurs in 'Galileo said that the earth moves' to be essentially like its occurrence in' "The earth" has eight characters'. Expressions under quotation are, according to Quine, referentially inert, i.e. they neither refer nor can be used to refer. Hence, in any utterance of 'The earth moves and Galileo said that the earth moves' only the first occurrence of 'the earth' is genuinely referential. But clearly, this theory is no less incredible than is Frege's; Davidson's objection is equally applicable here.

Research paper thumbnail of AI AGENTS

Research paper thumbnail of Towards a closer integration of finite domainpropagation and simplex-based algorithms

This paper describes our experience in implementing an industrial application using the finite do... more This paper describes our experience in implementing an industrial application using the finite domain solver of the ECL i PS e constraint logic programming (CLP) system, in conjunction with the mathematical programming (MP) system, FortMP. In this technique, the ECL i PS e system generates a feasible solution that is adapted to construct a starting point (basic solution) for the MP solver. The basic solution is then used as an input to the FortMP system to warm-start the simplex (SX) algorithm, hastening the solution of the linear programming relaxation, (LPR). SX proceeds as normal to find the optimal integer solution.

Research paper thumbnail of Nonsystematic Search and No-Good Learning

Journal of Automated Reasoning, 2000

Nonsystematic search algorithms seem, in general, to be well suited to large-scale problems with ... more Nonsystematic search algorithms seem, in general, to be well suited to large-scale problems with many solutions. However, they tend to perform badly for problems with few solutions, and they cannot be used for insoluble problems, since they are incomplete.

Research paper thumbnail of Another Point of Reference

Expressions are usually distinct from their semantics; that is, expressions themselves do not par... more Expressions are usually distinct from their semantics; that is, expressions themselves do not participate in their semantics. One exception is where expressions are quoted. The conjecture below is that there are other contexts in which expressions participate in their semantics, even though they are not quoted or mentioned in any way. Propositional attitudes are one example, and the way they contain singular propositions generates a number of questions, among them the following. • Do demonstratives and names contribute to ascribed beliefs in the same way? • What contribution does an indexical make to the content of a belief or a thought? • Does Semantic Relationism capture the content of a name when it occurs in ascribed beliefs? • If names have sense, can that sense be understood as a procedure rendered as a program? • Does machine learning show how the referent of a name can be learnt without invoking either sense or direct reference? A number of conjectures emerge from considering these questions, and it is shown that they can be implemented jointly in a consistent logical system.

Research paper thumbnail of Language of Thought and Cognitive Science

Fodor and Pylyshyn propose an approach to the study of mind where semantic concepts, with the exc... more Fodor and Pylyshyn propose an approach to the study of mind where semantic concepts, with the exception of reference, can have no fundamental explanatory role. 1 Their claim reflects a view of cognitive science where mental processes are computations over tokens of mental representations, i.e., over their physical renderings. These cause behaviour and provide an explanation of it. The problem, to be shown below, is that mental representations can have an ambiguous status depending on the context. Resolving the ambiguity is an intractable task. This threatens Fodor and Pylyshyn's approach to cognitive science.

Research paper thumbnail of Constraint logic programming for scheduling and planning

BT technology journal, 1995

Constraint Logic Programming languages are extensions of logic programming systems such as PROLOG... more Constraint Logic Programming languages are extensions of logic programming systems such as PROLOG with constraint-handling facilities. There have been two lines of development: systems such as the CLP(X) scheme JL87] and PROLOG III Col90] in which constraints are ...

Research paper thumbnail of Planning parallel actions

Artificial Intelligence, 1998

This paper presents an integrated view of a wide range of planning systems derived from different... more This paper presents an integrated view of a wide range of planning systems derived from different theoretical foundations. The work is motivated by the need to provide a clear foundation from which a systematic study of search and representation issues in planning can be conducted. An evolutionary path is identified which shows how the classical (state-based) planning strategy can be incrementally refined into strategies capable of generating parallel plans. This is achieved by considering a succession of planning strategies having a progressively deeper involvement with interval-based representations. Each strategy is defined in terms of a plan representation, truth criterion and an example plan generation procedure which maps out a clearly specified search graph. The capabilities and limitations of each strategy are compared. This approach enables much of the wisdo'm embedded in existing planners based on the specified strategies to be distilled and unified. The succession of planning strategies identified in this paper define a framework within which fundamental design issues can be considered such as the level of commitment a constraintposting planner should make during its search for a solution. The framework also highlights the need for practical planners to prevent synergistic interference between parallel actions in an efficient manner. @ 1998 Elsevier Science B.V.

Research paper thumbnail of Distributed optimisation: A case study of utilising teaching space in a college

This paper presents an approach to distributed optimisation applied to the problem of teaching sp... more This paper presents an approach to distributed optimisation applied to the problem of teaching space utilisation in a college. We describe the basic ingredients of the problem and analyse various solutions, some produced in a centralised environment and some in a distributed environment. The main aim is to investigate how distributed optimisation may be formulated. In particular we introduce a "broker"-based approach for interdepartmental sharing of resources, with a view to finding a reasonable compromise between allowing a degree of autonomy for individual departments and optimising the global usage of resources at the college level. Various results of the experiments based on different optimisation criteria and heuristics are presented and analysed. 1 Introduction The problem of teaching space utilisation(TSU) addresses the task of making effective use of teaching space within a distributed college environment [2, 3, 4, 6, 7]. This involves scheduling timetables and allocating reso...

Research paper thumbnail of A Decomposition-based Approach to Checking the Satisfiability of Temporal Database Query in Temporal Planning

Journal of electrical engineering and information science, 1999

This paper presents a method for increasing the efficiency of checking the satisfiability of a st... more This paper presents a method for increasing the efficiency of checking the satisfiability of a structure known as a temporal database query(TDBQ), which is an essential component of temporal planning. We develop a new "qualitative" strategy for decomposing a TDBQ into nearly-independent sub-TDBQ's, whose satisfiability can be checked separately; if all sub-TDBQ's are satisfiable, we use an efficient method of testing for global consistency. To ensure the correctness of the procedure we must impose certain restrictions on the temporal constraints used in specifying planning problems and action operators. But these do not present an awkward restriction on expressiveness. They do, however, lead to a significant reduction in the propagation of constraints and thus greatly enhance the performance of the temporal reasoning system.

Research paper thumbnail of The Scope, order, and distribution of English auxiliary verbs

Table of Contents Volume two.- A New Theory of English Auxiliaries.- Scope Ambiguities of Tense, ... more Table of Contents Volume two.- A New Theory of English Auxiliaries.- Scope Ambiguities of Tense, Aspect and Negation.- Generalized Categorial Grammars and the English Auxiliary.- Auxiliary and Copula Be in a Functional Grammar of English.- Explaining Auxiliary Order.- Semantic Explanations for the Syntax of the English Modals.- The Auxiliary System in Sranan.

Research paper thumbnail of Linguistic Categories: Auxiliaries and Related Puzzles

Language, 1985

In the English grammar lessons, will and shall are taught in schools and universities as modal ve... more In the English grammar lessons, will and shall are taught in schools and universities as modal verbs. Almost all famous grammarians confirm that will and shall are modal verbs. Modal verbs are considered as auxiliaries apart from the main or primary auxiliaries be, have, and do. Considering the definitions and characteristics of auxiliaries and inflections, a deep understanding of will and shall is required. This paper examines the definitions and characteristics of both auxiliaries and inflections and the uses of will and shall in order to know whether will and shall are auxiliaries or free inflections of the Future Tense. However it is worth mentioning that time is divided into past, present, and future. In modern English, almost grammarians say that there are two tenses in English namely present tense and past tense. According to them, the future tense does not exist. They believe so simply because there is no inflection for future tense; the futurity is expressed through modal verbs (will and shall). Generally speaking, modal auxiliaries help lexical verbs to express a variety of meanings, different attitudes, such as mood, aspect, etc. whereas inflections help verbs to express tenses. For instance,-ed is a bound inflection that helps regular verbs express the simple past tense. The-s is also a bound inflection that expresses the third person singular in the Simple Present Tense whereas-Ø is an invisible inflection which expresses the first persons (singular and plural), second persons (singular and plural), and the third person plural of the Simple Present Tense). Is there any inflection for the Future Tense? This paper is an attempt to answer this question.

Research paper thumbnail of Semantic Theory and Grammatical Structure

Aristotelian Society Supplementary Volume, 1980

I. Introduction. What we discern as the grammatical structure of a language may depend in part up... more I. Introduction. What we discern as the grammatical structure of a language may depend in part upon considerations of semantic theory. This is particularly true if the grammar is categorial, for such a grammar can be seen to have a special connection with formal ...

Research paper thumbnail of Constructivism and logical reasoning

Synthese, 1985

Cognitive development is typically thought to be a process which involves the acquisition of new ... more Cognitive development is typically thought to be a process which involves the acquisition of new concepts. As a child progresses from infancy to maturity, he shows an increasing ability to deal with complex situations, and it is natural to account for this in terms of the addition of ...

Research paper thumbnail of Application of the Generic Planning Architecture to Flight Allocation

Research paper thumbnail of An Empirical Study of Min-Conflict Hill Climbing and Weak Commitment Search

Research paper thumbnail of Restart-repair and Learning: An empirical study of single solution 3-SAT problems

The aim of this paper is to demonstrate that a particular non-systematic search algorithm based o... more The aim of this paper is to demonstrate that a particular non-systematic search algorithm based on restart-repair and learning no-goods can solve single solution 3-SAT problems efficiently. These problems are thought to present a severe challenge for algorithms of this sort since ...

Research paper thumbnail of On interpreting pronouns

Research paper thumbnail of Aircraft Allocation in a Parallel Constraint Logic Programming Environment

Research paper thumbnail of Anaphora, descriptions and discourse representations

Research paper thumbnail of Nogood Learning for Constraint Satisfaction

The basic algorithm is derived from the weak-commitment algorithm (WC) of Yokoo [17], which has b... more The basic algorithm is derived from the weak-commitment algorithm (WC) of Yokoo [17], which has been shown to outperform breakout and min-conflict backtracking on certain classes of problems. Weak-commitment search is that part of WC which results from removing the ...

Research paper thumbnail of Planning with constraints

... We shall survey some of the relevant considerations below, focusing specifically on the role ... more ... We shall survey some of the relevant considerations below, focusing specifically on the role of flexible heuristics. ... One area where the integration is likely to yield benefits is with respect to the treatment of both sofi and hard constraints, although this is a somewhat different matter ...

Research paper thumbnail of IQ-TREC: Temporal and Resource Reasoning for

Research paper thumbnail of A Planning Architecture using Temporal Constraint Solving

In this report we describe a generic planning architecture developed in the context of Constraint... more In this report we describe a generic planning architecture developed in the context of Constraint Logic Programming. Constraint-solving is used to handle both temporal and non-temporal rea-soning tasks that arise in planning. The architecture allows considerable ...

Research paper thumbnail of Guide to the Generic Planning Architecture

Research paper thumbnail of Subnet Generation Problem: A New Network Routing Problem

Lecture Notes in Computer Science, 2005

We introduce a new type of network routing problem, the subnet generation problem (SGP) which is ... more We introduce a new type of network routing problem, the subnet generation problem (SGP) which is a special case of the traffic placement problem (TPP). In the TPP, given (1) a network which consists of routers and links, and (2) a set of point-to-point traffic demands to be placed including finding feasible routes, the objective is to minimize the sum of costs of the unplaced demands subject to the Quality-of-Service routing constraints. The SGP is a TPP with an extra set of constraints that restricts the combinations of demands to be placed. In our SGP, each router has a fixed amount of information-gain that is to be transmitted to every other router in the subnet. A subnet is defined as any subset of the routers in the network. This means that every router in the subnet will have exactly the same total information-gain. The objective is to find a subnet that maximizes the total information-gain: there must be a demand with a valid path between every pair of routers in the subnet. The reason for creating demands among the routers arises from the fact that every node in a selected group of routers is required to be a client and a server. The figure below shows an example of a subnet and a path solution. I would like to thank Quanshi Xia and Christophe Guettier for their participation.