## Modelling Multicast QoS Routing by using Best-Tree Search in And-or Graphs and Soft Constraint Logic Programming (2007)

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Venue: | QAPL |

Citations: | 5 - 4 self |

### BibTeX

@MISC{Bistarelli07modellingmulticast,

author = {Stefano Bistarelli and Ugo Montanari and Francesca Rossi and Francesco Santini},

title = {Modelling Multicast QoS Routing by using Best-Tree Search in And-or Graphs and Soft Constraint Logic Programming },

year = {2007}

}

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### Abstract

We suggest a formal model to represent and solve the multicast routing problem in multicast networks. To attain this, we model the network adapting it to a weighted and-or graph, where the weight on a connector corresponds to the cost of sending a packet on the network link modelled by that connector. Then, we use the Soft Constraint Logic Programming (SCLP) framework as a convenient declarative programming environment in which to specify related problems. In particular, we show how the semantics of an SCLP program computes the best tree in the corresponding and-or graph: this result can be adopted to find, from a given source node, the multicast distribution tree having minimum cost and reaching all the destination nodes of the multicast communication. The costs on the connectors can be described also as vectors (multidimensional costs), each component representing a different Quality of Service metric value. Therefore, the construction of the best tree may involve a set of criteria, all of which are to be optimized (multi-criteria problem), e.g. maximum global bandwidth and minimum delay that can be experienced on a single link.

### Citations

8996 |
Introduction to Algorithms
- Cormen, Leiserson, et al.
- 2001
(Show Context)
Citation Context ...as Shortest-Path Tree (SPT), Minimum Spanning Tree (MST), Steiner Tree (ST), Constrained Steiner Tree (CST), and other miscellaneous trees [22]. Algorithms based on SPT (e.g. Dijkstra or Bellman-Ford =-=[11]-=-) aim to minimize the sum of the weights on the links from the source to each receiver, and if all the link cost one unit, the resulting tree is the least-hop one. The MST (e.g. Prim algorithm [11]) s... |

791 | Constraint logic programming: a survey
- Jaffar, Maher
- 1994
(Show Context)
Citation Context ...ng (SCLP) framework [2,4,12] as a convenient declarative programming environment in which to specify and solve such problem. SCLP programs are an extension of usual Constraint Logic Programming (CLP) =-=[14]-=- programs where logic programming is used in conjunction with soft constraints, that is, constraints which can be satisfied at a certain level. In particular, we will show how to represent an and-or g... |

740 |
OSPF version 2
- Moy
- 1991
(Show Context)
Citation Context ...(towards distinct group members) and global admission control of the distribution flow. Some of the approaches use a Steiner formulation [11] or extend existing algorithm to optimize the delay (MOSPF =-=[15]-=- is the multicast version of OSPF), while the Delay Variation Multicast Algorithm (DVMA) [18] computes a multicast tree with both bounded delay and bounded jitter. Also, delay-bounded and cost-optimiz... |

589 |
Principles of Artificial Intelligence
- Nilsson
- 1980
(Show Context)
Citation Context ...costs for the connectors. Generally, and-or graphs are used to model problem solving processes, and together with minimum cost solution graphs have been studied extensively in artificial intelligence =-=[19]-=-. Afterwards, we will propose the Soft Constraint Logic Programming (SCLP) framework [2,4,12] as a convenient declarative programming environment in which to specify and solve such problem. SCLP progr... |

255 |
A fast algorithm for Steiner trees
- Kou, Markowsky, et al.
- 1981
(Show Context)
Citation Context ...ed to support shared and heterogeneous reservation styles (towards distinct group members) and global admission control of the distribution flow. Some of the approaches use a Steiner tree formulation =-=[1]-=- or extend existing algorithm to optimize the delay (MOSPF [17] is the multicast version of OSPF), while the Delay Variation Multicast Algorithm (DVMA) [21] computes a multicast tree with both bounded... |

247 | Internet QoS: a big picture
- Xiao, Ni
- 1999
(Show Context)
Citation Context ...tion also require a certain timeliness of delivery (real-time applications), multicast routing has been clearly extended to include and guarantee QoS requirements; a global picture of QoS is given in =-=[24]-=-. In this case, the Constraint-Based multicast routing, the problem is to find the best distribution tree with respect to certain performance related constraints, to better utilize network resources a... |

189 |
Semiring-based constraint solving and optimization
- Bistarelli, Montanari, et al.
- 1997
(Show Context)
Citation Context ... is an instantiation of a more general one based on the notion of c-semiring [2,3]. 4 Soft Constraint Logic Programming The SCLP framework [2,4,12], is based on the notion of c-semiring introduced in =-=[3,8]-=-. A c-semiring S is a tuple 〈A, +, ×, 0, 1〉 where A is a set with two special elements (0, 1 ∈ A) and with two operations + and × that satisfy certain properties: + is defined over (possibly infinite)... |

102 | Constraint solving over semirings
- Bistarelli, Montanari, et al.
- 1995
(Show Context)
Citation Context ...refore, the cost of the tree in Fig. 3, with root node n2, is 17. In the next Sections we will show that this cost function is an instantiation of a more general one based on the notion of c-semiring =-=[2,3]-=-. 4 Soft Constraint Logic Programming The SCLP framework [2,4,12], is based on the notion of c-semiring introduced in [3,8]. A c-semiring S is a tuple 〈A, +, ×, 0, 1〉 where A is a set with two special... |

78 | Multicast Routing with End-to-End Delay and Delay Variation Constraints
- Rouskas, Baldine
- 1996
(Show Context)
Citation Context ...he approaches use a Steiner tree formulation [1] or extend existing algorithm to optimize the delay (MOSPF [17] is the multicast version of OSPF), while the Delay Variation Multicast Algorithm (DVMA) =-=[21]-=- computes a multicast tree with both bounded delay and bounded jitter. Also, delay-bounded and cost-optimized multicast routing can be formulated as a Steiner tree: an example approach is QoS-aware Mu... |

76 | Semiring frameworks and algorithms for shortest-distance problems
- Mohri
(Show Context)
Citation Context ...the links to use in the best tree. For this reason, we use the semiring structure (Sec. 4). An exhaustive explanation of the semiring framework approach for shortest-distance problems is presented in =-=[16]-=-. For example, if we are interested in maximizing the bandwidth of the distribution tree, we can use the c-semiring SBandwidth = 〈B ∪ {0, +∞}, max, min, 0, +∞〉 (otherwise, we could be interested in mi... |

67 | Multicast routing and its QoS extension: Problems, algorithms and protocols
- Wang, Hou
- 2000
(Show Context)
Citation Context ...ently distribute contents on behalf of applications asking for a certain timeliness of delivery: thus, multicast routing has naturally been extended to guarantee Quality of Service (QoS) requirements =-=[22]-=-. In this paper we suggest a formal model to represent and solve the multicast routing problem in multicast networks with QoS. For the representation we use and-or graphs [15] to model the network and... |

54 | Soft concurrent constraint programming
- Bistarelli, Montanari, et al.
- 2002
(Show Context)
Citation Context ...e future we plan to perform some experiments to directly test the computational complexity of our framework. Moreover, we plan to enrich this framework by using Soft Concurrent Constraint Programming =-=[7]-=- to handle the interactions among the routing devices and the receivers, and, consequently, we would like to introduce new “soft” operations (e.g. a retract of a constraint) to release the resources r... |

52 |
Semirings for Soft Constraint Solving and Programming. Number 2962 in LNCS
- Bistarelli
- 2004
(Show Context)
Citation Context ... we suggest a formal model to represent and solve the multicast routing problem in multicast networks with QoS. For the representation we use and-or graphs [15] to model the network and SCLP programs =-=[2,4,12]-=- on the graphs to compute the best tree according to QoS criteria. Given a multicast group of receiver nodes and a set of optimization objective functions, the multicast routing problem is the process... |

51 | QoS-aware multicast routing protocol
- Chen, Shavitt
- 2000
(Show Context)
Citation Context ...e with both bounded delay and bounded jitter. Also, delay-bounded and cost-optimized multicast routing can be formulated as a Steiner tree: an example approach is QoS-aware Multicast Routing Protocol =-=[10]-=- (QMRP). Other multicast QoS routing algorithms and related problems (entailing stability, robustness and scalability) are presented in [25], and we did not include them here for lack of space. Our so... |

47 |
RFC 2328: OSPF Version 2
- Moy
- 1998
(Show Context)
Citation Context ...ards distinct group members) and global admission control of the distribution flow. Some of the approaches use a Steiner tree formulation [1] or extend existing algorithm to optimize the delay (MOSPF =-=[17]-=- is the multicast version of OSPF), while the Delay Variation Multicast Algorithm (DVMA) [21] computes a multicast tree with both bounded delay and bounded jitter. Also, delay-bounded and cost-optimiz... |

46 | Semiring-based constraint logic programming: Syntax and semantics
- Bistarelli, Montanari, et al.
- 2001
(Show Context)
Citation Context ... we suggest a formal model to represent and solve the multicast routing problem in multicast networks with QoS. For the representation we use AND-OR graphs [13] to model the network and SCLP programs =-=[1, 4, 9]-=- on the graphs to compute the best tree according to QoS criteria. ⋆ Partially supported by Institute of Informatics and Telematics (IIT-CNR) Pisa, ItalysGiven a multicast group of receiver nodes and ... |

45 |
Steiner problem in networks: A survey. Networks
- Winter
- 1987
(Show Context)
Citation Context ...otal weight of the tree at the same time; at each step, the tree is augmented with an edge that contributes the minimum amount possible to the total cost of the tree, so the algorithm is greedy. A ST =-=[20]-=- is a tree which spans a given subset of vertices in the graph with the minimal total distance on its edges. If the subset matches the entire multicast group, ST problem reduces to MST. ST has been ex... |

38 | Compiling Semiring-based constraints with clp(FD,S
- Georget, Codognet
- 1998
(Show Context)
Citation Context ... we suggest a formal model to represent and solve the multicast routing problem in multicast networks with QoS. For the representation we use and-or graphs [15] to model the network and SCLP programs =-=[2,4,12]-=- on the graphs to compute the best tree according to QoS criteria. Given a multicast group of receiver nodes and a set of optimization objective functions, the multicast routing problem is the process... |

35 |
The ciao prolog system. reference manual
- Bueno, Cabeza, et al.
- 1997
(Show Context)
Citation Context ...0Mbps and a delay of 30msec. Other SCLP clauses can properly describe the structure of the tree we desire to search over the graph. We chose to represent an and-or graph with a program in CIAO Prolog =-=[9]-=-, a system that offers a complete Prolog system supporting ISO-Prolog, but, at the same time its modular design allows both restricting and extending the basic language. Thus, it allows both to work w... |

32 |
Optimizing Decision Trees Through Heuristically Guided Search
- Martelli, Montanari
- 1978
(Show Context)
Citation Context ...rvice (QoS) requirements [22]. In this paper we suggest a formal model to represent and solve the multicast routing problem in multicast networks with QoS. For the representation we use and-or graphs =-=[15]-=- to model the network and SCLP programs [2,4,12] on the graphs to compute the best tree according to QoS criteria. Given a multicast group of receiver nodes and a set of optimization objective functio... |

16 | Constraint-based routing in the internet: Basic principles and recent research
- Younis, Fahmy
- 2003
(Show Context)
Citation Context ...f routing algorithms that base path selection decisions on a set of requirements or constraints, in addition to the destination: constraints can be imposed by administrative policies, or by QoS needs =-=[25]-=-. The other intent of CBR is to increase the utilization of the network (CBR is a tool for Traffic Engineering [24,25]), and is a part of the global framework that provide Internet QoS [24]. Multicast... |

15 | A Formal Basis for Reasoning on Programmable QoS
- Nicola, Ferrari, et al.
- 2003
(Show Context)
Citation Context ...ich have more than one atom in their body. In this paper, we use instead clauses closer to logic programming, and we represent trees instead of paths. Related formal approaches dealing with QoS, e.g. =-=[18]-=- and [13], adopt a hypergraph model in joint with semirings too, but the minimal path between two nodes (thus, not over an entire tree) is computed via a graphical calculous instead of SCLP. This pape... |

12 | Soft constraint logic programming and generalized shortest path problems
- Bistarelli, Montanari, et al.
(Show Context)
Citation Context ...st tree that ensures QoS requirements on the corresponding network. Since several QoS parameters express the cost of a link at the same time, this problem can be addressed as a multi-criteria problem =-=[6]-=-, where the combination of the costs is done via an operator which is more general than the usual sum of the link weights. This extension can be easily cast within the SCLP programming framework, beca... |

11 |
Translation of decision tables
- Pooch
- 1974
(Show Context)
Citation Context ...me time. Even if in this paper we have applied SCLP programs over and-or graph to find the best multicast distribution tree, the same framework could be used also to solve problems on decision tables =-=[20]-=-, by translating them into and-or graphs, or even other dynamic programming problems. Decision tables are widely used in many data processing applications for specifying which action must be taken for... |

3 |
U.: Form dynamic programming to search algorithms with functional costs
- Martelli, Montanari
- 1975
(Show Context)
Citation Context ...ombination of the outcomes of a set of condition tests. An important problem is to derive from a given decision table a decision tree which is optimal in some specified sense. Previous works (such as =-=[12]-=-) introduced a general model of dynamic programming based on AND-OR graphs and showed that each dynamic programming problem could be reduced to the problem of finding an optimal solution tree in an AN... |

2 |
SCLP Semantics for (Multi-Criteria) Shortest Path Problems
- Bistarelli, Montanari, et al.
- 1999
(Show Context)
Citation Context ...hile the partial order defined by + operation (see Section 4), is used to compare the costs. The work presented and suggested in this paper extends some results on shortest path problems presented in =-=[5]-=- and [6]. In these two works, the main idea concerned the use of non-linear clauses in SCLP, that is, clauses which have more than one atom in their body. In this paper, we use instead clauses closer ... |

2 | Shreq: Coordinating application level qos
- Hirsch, Tuosto
(Show Context)
Citation Context ...more than one atom in their body. In this paper, we use instead clauses closer to logic programming, and we represent trees instead of paths. Related formal approaches dealing with QoS, e.g. [18] and =-=[13]-=-, adopt a hypergraph model in joint with semirings too, but the minimal path between two nodes (thus, not over an entire tree) is computed via a graphical calculous instead of SCLP. This paper is orga... |

1 |
problem in networks: a survey, Netw
- Winter, Steiner
- 1987
(Show Context)
Citation Context ...otal weight of the tree at the same time; at each step, the tree is augmented with an edge that contributes the minimum amount possible to the total cost of the tree, so the algorithm is greedy. A ST =-=[23]-=- is a tree which spans a given subset of vertices in the graph with the minimal total distance on its edges. If the subset matches the entire multicast group, ST 4sBistarelli et al problem reduces to ... |